With the advent of inexpensive digital color printers, methods and systems of color digital halftoning have become increasingly important in the reproduction of printed or displayed images possessing continuous color tones. It is well understood that most digital color printers operate in a binary mode, i.e., for each color separation, a corresponding colorant spot is either printed or not printed at a specified location or pixel. Digital halftoning controls the printing of colorant spots, where the spatial averaging of the printed colorant spots by either a human visual system or a viewing instrument, provides the illusion of the required continuous color tones. In the art of printing, the color tone that results from the overlay of the halftone spots from multiple colorants is often referred to as “process color.” Color separations can be thought of as multiple channels that can be used to define the color of an image. Color separations are sometimes called colorant separations because they are used to specify amounts of colorants required to achieve a target perception of color.
The most common halftone technique is screening, which compares the required continuous tone colorant level of each pixel for each color separation with one or more predetermined threshold levels. The predetermined threshold levels are typically defined for a rectangular cell that is tiled to fill the plane of an image, thereby forming a halftone screen of threshold values. At a given pixel if the required continuous tone colorant level is darker than the threshold halftone level, a colorant spot is printed at that specified pixel. Otherwise the colorant spot is not printed. The output of the screening process is a binary pattern of multiple small “dots”, which are regularly spaced as is determined by the size, shape, and tiling of the halftone cell. In other words, the screening output halftone image separation, as a two-dimensionally repeated pattern, possesses two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screen.
It is understood in the art that the distribution of printed pixels in a color halftone image separation depends on the design of the halftone screen. For clustered-dot halftone screens, all printed pixels formed using a single halftone cell typically group into one or more clusters. If a halftone cell only generates a single cluster, it is referred to as a single-dot halftone or single-dot halftone screen. Alternatively, halftone screens may be dual-dot, tri-dot, quad-dot, or the like.
While halftoning is often described in terms of halftone dots, it should be appreciated that idealized halftone dots can possess a variety of shapes that include rectangles, squares, lines, circles, ellipses, “plus signs”, X-shapes, pinwheels, and pincushions, and actual printed dots can possess distortions and fragmentation of those idealized shapes introduced by digitization and the physical printing process. Various digital halftone screens having different shapes and angles are described in “An Optimum Algorithm for Halftone Generation for Displays and Hard Copies”, by T. M. Holladay, Proc. Soc. for Information Display, 21, p. 185, 1980.
A common problem that arises in digital color halftoning is the manifestation of moiré patterns. Moiré patterns are undesirable interference patterns that occur when two or more color halftone image separations are printed over each other. Since color mixing during the printing process is a non-linear process, frequency components other than the fundamental frequencies and harmonics of the individual color halftone image separations can occur in the final printout. For example, if an identical halftone screen is used for two color image separations, theoretically, there should be no moiré patterns. However, any slight misalignment between the two color halftone image separations occurring from an angular difference and/or a scalar difference will result in two slightly different fundamental frequency vectors. Due to nonlinear color mixing, the difference in frequency vectors produces a beat frequency which will be visibly evident as a very pronounced moiré interference pattern in the output. Additionally, lateral displacement misregistration can result in significant color shifts if an identical halftone screen is used for two color image separations. To avoid, for example, two-color moiré patterns and other color shifts due to misalignment and misregistration, or for other reasons, different halftone screens are commonly used for different color image separations, where the fundamental frequency vectors of the different halftone screens are separated by relatively large angles. Therefore, the frequency difference between any two fundamental frequencies of the different screens will be large enough so that no visibly objectionable moiré patterns are produced.
In selecting different halftone screens, for example for three color image separations, it is desirable to avoid any two-color moiré as well as any three-color moiré. It is well known that in the traditional printing industry that three halftone screens, which can be constructed by halftone cells that are square in shape and identical, can be placed at 15°, 45°, and 75°, respectively, from a point and axis of origin, to provide the classical three-color moiré-free solution. This is described in “Principles of Color Reproduction”, by J. A. G. Yule, John Wiley & Sons, N.Y., 1967.
For digital halftoning, the freedom to select a rotation of a halftone screen is limited by the raster structure, which defines the position of each pixel. Since tan(15°) and tan(75°) are irrational numbers, a halftone screen at a rotation of 15° or 75° cannot be implemented exactly in digital halftoning. To this end, some methods have been proposed to provide approximate instead of exact moiré-free solutions. For example, in U.S. Pat. No. 4,916,545, moiré is suppressed by randomly varying the dot fonts that are used to write successive halftone dots in the screened image. In U.S. Pat. No. 5,442,461, strips of a rational angled screen are concatenated to approximate an irrational angled screen. Errors which accumulate with each successive pixel are corrected by occasionally jumping to a new point in the strip. However, all these approximate solutions result in some halftone dots having centers that do not lie directly on addressable points, or on the pixel positions defined by the raster structure. Therefore, the shape and center location varies from one halftone dot to another. Consequently, additional interference or moiré between the screen frequencies and the raster frequency can occur. In another approach, U.S. Pat. No. 5,371,612 discloses a moiré prevention method to determine screen angles and sizes that is usable solely for square-shaped, halftone screens.
Notably, DOD screens are known to produce much finer textures than conventional rotated dot screens. While rotated dot screens have the advantage of insensitivity to registration, they do have the negative drawback of possessing a texture frequency component, i.e. the rosette, that is roughly half of the halftone frequency. Conversely, periodic dot-off-dot screens have the desirable attribute of possessing an apparent frequency that is significantly higher than the single-separation halftone frequency. If a printer can achieve tight color-to-color registration, dot-off-dot screens can generate acceptable textures using very low frequency halftones, which could drastically reduce spatial noise and print-to-print color variation. Furthermore, it could also improve the basic appearance of the halftone texture because there would not be rosettes at ½ the halftone frequency. In addition to texture improvements, dot-off-dot halftones produce a larger gamut than rotated halftone screens.
The above indicated patents and citations provide a background basis for the disclosure as taught in the specification which follows below, and further for each of the patents and citations above, the disclosures therein are totally incorporated herein by reference in their entirety for their teachings.
As provided herein, there are supplied teachings to systems and methods that utilize a 3-colorant DOD periodic halftone geometry.